SMIP16 Seminar Proceedings 9 FRAGILITY CURVES FOR THE RAPID POSTEARTHQUAKE SAFETY EVALUATION OF BRIDGES Roy A. Imbsen 1 , Shah Vahdani 2 , M. Saiid Saiidi 3 , Hassan Sedarat 1 , and Farid Nobari 1 1 SC Solutions, Inc. Sunnyvale 2 Applied GeoDynamics, Inc., El Cerrito 3 Infrastructure Innovation, LLC, Reno Abstract A new procedure for rapid post-earthquake safety evaluation of bridges has been developed, using existing strong motion records, fragility curves and ground motion data immediately available following an earthquake that will provide the engineer or person directly in charge of the bridge to make a more informed decision to close or keep a bridge open to traffic. The recently constructed Carquinez I80 West Bridge (Alfred Zampa Memorial Bridge) was selected to demonstrate the procedure. This paper describes the detailed time history finite element analysis conducted using strong motion data for the 26 scenario earthquake events and the development of the fragility curves using shake table test results on reinforced concrete columns tested through five damage states to final failure. Fragility functions are developed for various seismic parameters for each damage state and calibrated for maximum drift ratios for inclusion into the rapid safety evaluation of the Carquinez Bridge. Introduction This study, entitled Rapid Post-Earthquake Safety Evaluation of the New Carquinez Bridge Using Fragility Curves and Recorded Strong-Motion Data is part of the Data Interpretation Project of the California Strong Motion Instrumentation Program (CSMIP) in the Department of Conservation (DOC) California Geological Survey. The purpose of this project is to accelerate the application of the strong-motion data in reducing risk due to the strong earthquake shaking which occurs in California. Overview of the Safety Evaluation Procedure The application of the procedure undertaken in this study is to provide for the selected New Carquinez Bridge, as shown in Figure 1, the ability to assess the damage immediately following an earthquake using the ground motion parameters of the earthquake event and fragility curves developed for the bridge so that a decision can be made on the continued use or closure of the bridge.
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SMIP16 Seminar Proceedings
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FRAGILITY CURVES FOR THE RAPID POSTEARTHQUAKE SAFETY
EVALUATION OF BRIDGES
Roy A. Imbsen1, Shah Vahdani2, M. Saiid Saiidi3, Hassan Sedarat1, and Farid Nobari1
1SC Solutions, Inc. Sunnyvale
2Applied GeoDynamics, Inc., El Cerrito 3 Infrastructure Innovation, LLC, Reno
Abstract
A new procedure for rapid post-earthquake safety evaluation of bridges has been
developed, using existing strong motion records, fragility curves and ground motion data
immediately available following an earthquake that will provide the engineer or person directly
in charge of the bridge to make a more informed decision to close or keep a bridge open to
traffic. The recently constructed Carquinez I80 West Bridge (Alfred Zampa Memorial Bridge)
was selected to demonstrate the procedure. This paper describes the detailed time history finite
element analysis conducted using strong motion data for the 26 scenario earthquake events and
the development of the fragility curves using shake table test results on reinforced concrete
columns tested through five damage states to final failure. Fragility functions are developed for
various seismic parameters for each damage state and calibrated for maximum drift ratios for
inclusion into the rapid safety evaluation of the Carquinez Bridge.
Introduction
This study, entitled Rapid Post-Earthquake Safety Evaluation of the New Carquinez
Bridge Using Fragility Curves and Recorded Strong-Motion Data is part of the Data
Interpretation Project of the California Strong Motion Instrumentation Program (CSMIP) in the
Department of Conservation (DOC) California Geological Survey. The purpose of this project is
to accelerate the application of the strong-motion data in reducing risk due to the strong
earthquake shaking which occurs in California.
Overview of the Safety Evaluation Procedure
The application of the procedure undertaken in this study is to provide for the selected
New Carquinez Bridge, as shown in Figure 1, the ability to assess the damage immediately
following an earthquake using the ground motion parameters of the earthquake event and
fragility curves developed for the bridge so that a decision can be made on the continued use or
closure of the bridge.
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Figure 1: Aerial View of the New Carquinez Bridge
Background
SC Solutions (SCS) was tasked to develop a system to improve the current Caltrans rapid
post-earthquake decision making process for critical bridges. Immediately after any earthquake,
Caltrans has to make decisions about the post-earthquake conditions of bridges. The decision
making process will be based on the magnitude of the earthquake event, location of a bridge,
instrument data, the understanding of the performance of the bridge in the subject earthquake,
and factors related to risk and consequences. Most of the critical bridges that are in high seismic
zones are instrumented. These instrument data are monitored in real time and can be used for
this decision making process. The foundation or free field ground motions near the bridge and
some of the structural performance can be obtained immediately after an earthquake. However,
this limited instrument data doesn’t provide adequate information about the conditions of all
critical components of bridges immediately after an event. Therefore, additional understanding
of the bridge performance and fragility functions should be developed for each of these critical
bridges to assist the post-earthquake decision making process.
To develop fragility functions, first a set of pre-earthquake scenario events must be
selected based on the location of the bridge and the active faults in the vicinity of the bridge site.
For this task SC Solution proposed to use the New Carquinez Bridge for the case study. After
selecting a set of scenario earthquakes for the New Carquinez Bridge, the existing SCS bridge
model could be used to simulate the effects of these ground motions to understand the
performance of each critical component in the bridge. After conducting these pre-earthquake
seismic analyses, a relationship can be developed between the earthquake intensity parameter
(e.g. magnitude, distance and spectral acceleration) and the primary response parameter of a
critical component.
As one example, the primary response parameter can be a drift for a critical tower. Based
on the primary response parameter value, a damage index (or damage potential) can be
developed for each critical component. This damage potential can be related to the seismic
intensity parameter as a fragility function for each critical component.
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Pre-Event Data Processing
Figure 2: Pre-Event Data Processing
As shown in Figure 2, prior to an event, several automated procedures will be
completed and compiled in a “Bridge Seismic Assessment” report, as a reference document for
Caltrans decision making, after an event. The steps include the following:
a. Establish Scenario Earthquakes
To develop fragility functions, a set of pre-earthquake scenario events must be selected
based on the location of the bridge and the active faults in the vicinity of the bridge site. For the
purpose of this project, 26 sets of scenario ground motions were generated based on different
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magnitude earthquakes on regional faults. These motions ranged from low fault activity and
spectral acceleration, through Design Spectra, and spectral acceleration values both less than and
greater than design levels prescribed for the site. The characteristics of each motion were
identified by moment magnitude (Mw), distance to the fault (R), and spectral acceleration (Sa).
b. Develop Input Ground Motions at the Bridge Site
Using the available site specific ground motion, generation tools and design spectra, the SSI
analytical model customized for the Carquinez site was used to bring the scenario earthquakes to
the site and to generate scattered motions.
c. Dynamic Analyses of Bridge under Scenario Ground Motions (Demand)
The existing detailed Finite Element model of the New Carquinez Bridge [13, 21, 29],
developed by SCS, was used in the demand analyses subjected to the scenario ground motions.
Drift values of the critical components of the bridge were related to the motion characteristics
(Mw, R, Sa). For each critical component, a primary response parameter should be identified. In
this project, the proposed approach and scope-of-work is demonstrated for Tower 3 drift as the
primary response parameter to reflect the damage state of Critical Tower Components, as an
example of the process. This methodology can be applied to different primary response
parameters to reflect damage status of other critical components.
d. Pushover Analysis (Capacity)
A Finite Element model of Tower 3 was used to perform pushover analysis. Values of drift
and strain (concrete and reinforcement) were extracted and correlated.
e. Evaluation of Tower Drift and Component Damage (relationship between demand and
capacity)
Governing tower drifts as the primary response parameters were documented vs. motion
characteristics (Mw, R, and Sa), and finally a series of relationships between the motion
characteristics (Mw, R, and Sa), Tower Drift, and strain values (damage) of the critical tower
were generated.
f. Develop Fragility Data versus Earthquake Intensity and Tower Drift
Based on the analyses, the following response parameters were related to the scenario
earthquake intensity, fault, and distance to site:
Relation between damage states (DS) and strain (Fragility),
Relation between strain and drift (pushover analysis)
Using the above, obtain Relation between damage state (DS) and drift (Fragility),
Relation between (Mw, R, Sa) and drift (26 time-history analyses)
Description of the New Carquinez Bridge and Local Seismic Design Hazard
Description
The New Carquinez Bridge spans the Carquinez Strait with a 2,388 ft. main span
bounded by a south span (towards Oakland) of 482 ft. and a north span (towards Sacramento) of
594 ft. as shown in Figure 3. The principal components of this suspension bridge include
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reinforced concrete towers supported on large-diameter concrete pile foundations, parallel-wire
cables, gravity anchorages, and a closed orthotropic steel box deck system. The main concrete
towers are approximately 400 ft. tall, and are tied together with a strut below the deck and upper
strut between the cable saddles as shown in the Typical Section view included in Figure 3. The
lower strut supports the deck vertically using two rocker links and transversely through a shear
key.
Figure 3: General Plan
Local Seismic Design Hazard
The bridge site, located approximately twenty miles northeast of San Francisco, is located
in an active seismic zone. Seismic hazard assessments have shown that the site could be subject
to strong ground motions originating on the San Andreas Fault, the Hayward Fault, Concord-
Green Valley Fault, Napa Valley Fault, and the Franklin Fault. However, studies have shown
that the Hayward fault, Concord-Green Valley fault system, and the Napa Valley seismic zones
are the dominant sources of seismic hazard for the bridge’s frequency range.
The seismic design of the New Carquinez Bridge considers both the Safety
Evaluation Earthquake (SEE) and the lower level Functional Evaluation Earthquake (FEE).
Caltrans performance requirements for these events are higher than the minimum level
required for all transportation structures but below that required for an Important Bridge. As
much as possible, the Important Bridge criteria are to be met for the Safety Evaluation
Earthquake (SEE) corresponding to a maximum credible event which has a mean return
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period in the range of about 1,000 to 2,000 years. In this earthquake, the bridge can be
subject to primarily "minor" damage with some "repairable" damage to piles, pile caps and
anchorage blocks and still remain open.
Structural Analysis
A detailed finite element model of the New Carquinez Bridge was developed based on
the marked up drawings [10], using the ADINA FE program [31]. All structural components of
the new Carquinez Bridge were explicitly modeled. A cross-section of the steel box girders and
the bulkhead details are shown in Figure 4. The side elevation view is shown in Figure 5. The
key structural components that were included in the global FE model are summarized in Table 1.
Suspension bridges belong to a category of bridges that are highly nonlinear in geometry and
therefore, during the construction simulation and for their seismic evaluation, large displacement
capability was included in the analysis. Geometry iteration was used for the construction
sequence of the NCB FE detailed model [7, 22].
Figure 4: Detailed FE Model of the New Carquinez Bridge (Alfred Zampa Memorial Bridge)
Figure 5: Elevation View of Detailed Model
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Pushover Analysis of Tower 3 (Capacity Calculation) - Drift-Strain Curves
The stand-alone FE model of Tower T3 was developed with a fixed base. The pushover
profile is proportional to the first longitudinal mode of vibration for the tower, which was
obtained from the global model. The main reason to perform pushover analysis is to obtain
drift-strain curves (capacity), which will be used as an input to the fragility analysis.
Table 1: Key Structural Components [29]
Component Description / Model
Main Cables 37-strand cables with 232-wires per strand
Linear elastic beam elements with (partially non-composite moment of
inertia)
Hangers (suspenders) four galvanized structural steel ropes
Linear elastic truss elements
Towers Reinforced concrete box section
Localized plasticity at the location of plastic hinges
ADINA moment-curvature beam elements
Superstructure Orthotropic steel deck
8-noded shell elements with orthotropic properties
Rocker Links Steel rocker
Beam elements
Anchorages at the
North and South sides
Reinforced concrete
Rigid links
Piles Reinforced concrete
Moment-curvature beam elements
SSI modeling at piles PY
Nonlinear plastic truss elements
TZ and QZ
Nonlinear elastic spring elements
SSI modeling at
anchorages
Soil impedance
General elements: Stiffness, damping and mass matrices
Force-Displacement Curves from Pushover Analysis
The pushover analysis of Tower T3 was performed using the first longitudinal mode of
the tower. The inflection point location varies as the push forces increase. The force-
displacement of the tower is shown in Figure 6. The values of strain in confined concrete and
steel are also shown in this figure. The steel and concrete strain values along with the location of
the point of inflection are summarized in Table 2. The steel and concrete strain limits, based on
the design criteria [6] are 0.012, and 0.06 for concrete and steel, respectively. The steel strain
reached its limit, before the concrete, and at about a 6-ft displacement at the top of the tower.
The maximum relative top-to-bottom displacement of tower T3 from the PS&E analysis is 1.45-
ft [8].
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Figure 6: Total Base Shear - Displacement Relationships of Tower T3
Nonlinear Dynamic Analyses of the Detailed Model of the NCB – (Mw, R)-Strain Relation
In order to obtain a relationship between ground motion characteristics (Mw, R) and
damage (from fragility analysis), the relationship between the ground motion characteristics
(Mw, R) and the strain in concrete and steel should be obtained first. The relationship between
the capacity drift and strain was obtained from the pushover analysis. In this study, the demand
values which are the relationship between the ground motion characteristics (Mw, R) and drift
has been obtained from 26 nonlinear time-history analyses for the 26 scenario ground motions.
The relationship between the ground motion characteristics (Mw, R) and strain can be obtained
by combining the results obtained from the pushover analysis and time-history analyses, as
described Table 3 and Figure 7.
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Table 2: Force-Displacement-Strain Relationships of Tower T3
step
relative
displacement (ft)
lower strut to base
Δ
relative
displacement (ft)
upper strut to
base Δ
PI (ft) base shear (kip) strains at base
1.01 0.15 0.33 112.32 1.61E+03 6.18E-05 9.06E-04
1.02 0.30 0.66 112.32 3.23E+03 -4.80E-04 1.10E-03
1.03 0.44 0.98 112.32 4.83E+03 -1.06E-03 1.25E-03
1.04 0.59 1.31 112.32 6.44E+03 -1.66E-03 1.39E-03
1.05 0.74 1.64 112.22 7.93E+03 -2.89E-03 1.60E-03
1.06 0.89 1.97 111.35 8.61E+03 -6.09E-03 1.98E-03
1.07 1.03 2.30 110.17 8.96E+03 -1.04E-02 2.35E-03
1.08 1.18 2.62 108.89 9.15E+03 -1.54E-02 2.76E-03
1.09 1.33 2.95 107.64 9.31E+03 -2.04E-02 3.22E-03
1.1 1.48 3.28 106.42 9.44E+03 -2.54E-02 3.69E-03
1.11 1.62 3.61 105.23 9.58E+03 -3.02E-02 4.12E-03
1.12 1.77 3.94 104.08 9.73E+03 -3.48E-02 4.50E-03
1.13 1.92 4.27 102.97 9.85E+03 -3.94E-02 4.88E-03
1.14 2.07 4.59 101.88 9.99E+03 -4.38E-02 5.23E-03
1.15 2.21 4.92 100.82 1.01E+04 -4.84E-02 5.57E-03
1.16 2.36 5.25 99.79 1.02E+04 -5.29E-02 5.91E-03
1.17 2.51 5.58 98.79 1.03E+04 -5.79E-02 6.28E-03
1.18 2.66 5.91 97.80 1.04E+04 -6.29E-02 6.66E-03
1.19 2.81 6.23 96.84 1.05E+04 -6.81E-02 7.04E-03
1.2 2.95 6.56 95.90 1.06E+04 -7.35E-02 7.41E-03
1.21 3.10 6.89 94.98 1.07E+04 -7.88E-02 7.79E-03
1.22 3.25 7.22 94.07 1.08E+04 -8.42E-02 8.17E-03
1.23 3.40 7.55 93.18 1.09E+04 -8.97E-02 8.56E-03
1.24 3.54 7.87 92.28 1.10E+04 -9.53E-02 8.96E-03
1.25 3.69 8.20 91.40 1.10E+04 -1.01E-01 9.35E-03
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Table 3: Ground Motion (M/R) – Relative Drift at the Top of Tower and at PI – Strain in Steel
and Concrete at the Base of the Tower
North-West Leg combine Pushover - TH
strain at the base Relative Drift
@ Top
Relative Drift
@ PI
GM
run
ID
Scena
rio RSN Ground Motion Name M
R
(km) (ft) (ft) steel concrete
1 1 1176 1999 Kocaeli
Turkey 7.51 1.38 1.31 0.39 -1.655E-03 1.387E-03
2 3 1244 1999 Chi-Chi
Taiwan 7.62 9.94 1.43 0.43 -2.086E-03 1.461E-03
3 16 8099 2011 Christchurch
New Zealand 6.2 17.86 0.40 0.12 -5.989E-05 9.496E-04